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Development of percentile estimation formula for skewed distribution

Zhou Yun Hou Wei Qian Zhong-Hua He Wen-Ping

Development of percentile estimation formula for skewed distribution

Zhou Yun, Hou Wei, Qian Zhong-Hua, He Wen-Ping
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  • Order statistics establishes a relation between the position of the ranked data and corresponding cumulative probability, so it can be used to estimate the cumulative probability. Owing to the fact that different climatological data have different skewness degrees, in this paper, according to the cumulative probability function under the skewed distribution conditions, we perform theoretical analysis and numerical simulation to establish the position parameters of the regression model which are related to skewness index, then give an amperic percentile formula under the skewed distribution. By using the data about the summer temperature in global from 1980 to 2009, we compare the positions of ranked data corresponding to the 90th percentile, which are obtained by this formula and Jenkinsons formula.
    • Funds:
    [1]

    Jenkinson A F 1977 Synoptic Climatol. Branch Memo 58 41

    [2]

    Horton E B, Folland C K, Parker D E 2001 Climatic Change 50 267

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    Bonsal B R, Zhang X, Vincent L A, Hogg W D 2001 J. Climate 14 1959

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    Feng G L, Gong Z Q, Zhi R 2008 Acta Meteor. Sin. 66 892 (in Chinese) [封国林、龚志强、支 蓉 2008 气象学报 66 892]

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    Gong Z Q, Wang X J, Zhi R, Feng G L 2009 Acta Phys. Sin. 58 4342 (in Chinese) [龚志强、王晓娟、支 蓉、封国林 2009 物理学报 58 4342]

    [10]

    Feng G L, Wang Q G, Hou W, Gong Z Q, Zhi R 2009 Acta Phys. Sin. 58 2853 (in Chinese) [封国林、王启光、侯 威、龚志强、支 蓉 2009 物理学报 58 2853]

    [11]
    [12]
    [13]

    Folland C K, Anderson C W 2002 J. Climate 15 2954

    [14]

    Makkonen L 2005 J. Appl. Meteor. Climatol. 45 334

    [15]
    [16]

    Goel N K, De M 1993 Stoch. Hydrol. Hydraul. 7 1

    [17]
    [18]

    Hou W, Yang P, Feng G L 2008 Acta Phys. Sin. 57 3932 (in Chinese) [侯 威、杨 萍、封国林 2008 物理学报 57 3932]

    [19]
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    Zhang D Q, Qian Z H 2008 Acta Phys. Sin. 57 4634 (in Chinese)[章大全、钱忠华 2008 物理学报 57 4634]

    [22]

    Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Nonlinear Theory and Methods on Spatial-temporal Distribution of the Observational Data (Beijing: China Metrological Press) (in Chinese)[封国林、董文杰、龚志强、侯威、万仕全、支 蓉 2006 观测数据非线性时空分布理论和方法 (北京:气象出版社)]

    [23]
    [24]

    He W P, Feng G L, Dong W J, Li J P 2005 Chin. Phys. B 14 21

    [25]
    [26]
    [27]

    He W P,Feng G L, Wu Q, Wan S Q, Chou J F 2008 Nonlin. Proc. Geophys. 15 601

    [28]

    Feng G L, Yang J, Wan S Q, Hou W, Zhi R 2009 Acta Meteor. Sin. 67 61 (in Chinese) [封国林、杨 杰、万仕全、侯 威、支 蓉 2009 气象学报 67 61 ]

    [29]
    [30]
    [31]

    Feng G L, Gao X Q, Dong W J, Li J P 2008 Chaos Solitons Fract. 37 487

    [32]

    Feng G L, Gong Z Q, Zhi R, Zhang D Q 2008 Chin. Phys. B 17 2745

    [33]
    [34]

    Qian Z H, Feng G L, Gong Z Q 2010 Acta Phys. Sin. 59 7498 (in Chinese) [钱忠华、封国林、龚志强 2010 物理学报 59 7498 ]

    [35]
    [36]

    Chen X R 2009 Advanced Mathematical Statistics (Hefei: University of Science and Technology of China Press) p164 (in Chinese) [陈希孺 2009高等数理统计学(合肥:中国科学技术大学出版社)第164页]

    [37]
    [38]
    [39]

    Zhang L, Zhang D Q, Feng G L 2010 Acta Phys. Sin. 59 5897 (in Chinese) [张 璐、章大全、封国林 2010 物理学报 59 5897]

  • [1]

    Jenkinson A F 1977 Synoptic Climatol. Branch Memo 58 41

    [2]

    Horton E B, Folland C K, Parker D E 2001 Climatic Change 50 267

    [3]
    [4]
    [5]

    Bonsal B R, Zhang X, Vincent L A, Hogg W D 2001 J. Climate 14 1959

    [6]
    [7]

    Feng G L, Gong Z Q, Zhi R 2008 Acta Meteor. Sin. 66 892 (in Chinese) [封国林、龚志强、支 蓉 2008 气象学报 66 892]

    [8]
    [9]

    Gong Z Q, Wang X J, Zhi R, Feng G L 2009 Acta Phys. Sin. 58 4342 (in Chinese) [龚志强、王晓娟、支 蓉、封国林 2009 物理学报 58 4342]

    [10]

    Feng G L, Wang Q G, Hou W, Gong Z Q, Zhi R 2009 Acta Phys. Sin. 58 2853 (in Chinese) [封国林、王启光、侯 威、龚志强、支 蓉 2009 物理学报 58 2853]

    [11]
    [12]
    [13]

    Folland C K, Anderson C W 2002 J. Climate 15 2954

    [14]

    Makkonen L 2005 J. Appl. Meteor. Climatol. 45 334

    [15]
    [16]

    Goel N K, De M 1993 Stoch. Hydrol. Hydraul. 7 1

    [17]
    [18]

    Hou W, Yang P, Feng G L 2008 Acta Phys. Sin. 57 3932 (in Chinese) [侯 威、杨 萍、封国林 2008 物理学报 57 3932]

    [19]
    [20]
    [21]

    Zhang D Q, Qian Z H 2008 Acta Phys. Sin. 57 4634 (in Chinese)[章大全、钱忠华 2008 物理学报 57 4634]

    [22]

    Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Nonlinear Theory and Methods on Spatial-temporal Distribution of the Observational Data (Beijing: China Metrological Press) (in Chinese)[封国林、董文杰、龚志强、侯威、万仕全、支 蓉 2006 观测数据非线性时空分布理论和方法 (北京:气象出版社)]

    [23]
    [24]

    He W P, Feng G L, Dong W J, Li J P 2005 Chin. Phys. B 14 21

    [25]
    [26]
    [27]

    He W P,Feng G L, Wu Q, Wan S Q, Chou J F 2008 Nonlin. Proc. Geophys. 15 601

    [28]

    Feng G L, Yang J, Wan S Q, Hou W, Zhi R 2009 Acta Meteor. Sin. 67 61 (in Chinese) [封国林、杨 杰、万仕全、侯 威、支 蓉 2009 气象学报 67 61 ]

    [29]
    [30]
    [31]

    Feng G L, Gao X Q, Dong W J, Li J P 2008 Chaos Solitons Fract. 37 487

    [32]

    Feng G L, Gong Z Q, Zhi R, Zhang D Q 2008 Chin. Phys. B 17 2745

    [33]
    [34]

    Qian Z H, Feng G L, Gong Z Q 2010 Acta Phys. Sin. 59 7498 (in Chinese) [钱忠华、封国林、龚志强 2010 物理学报 59 7498 ]

    [35]
    [36]

    Chen X R 2009 Advanced Mathematical Statistics (Hefei: University of Science and Technology of China Press) p164 (in Chinese) [陈希孺 2009高等数理统计学(合肥:中国科学技术大学出版社)第164页]

    [37]
    [38]
    [39]

    Zhang L, Zhang D Q, Feng G L 2010 Acta Phys. Sin. 59 5897 (in Chinese) [张 璐、章大全、封国林 2010 物理学报 59 5897]

  • [1] Measurement of Magnetically Insensitive State Coherent Time in Blue Dipole Trap. Acta Physica Sinica, 2020, (): . doi: 10.7498/aps.69.20192001
    [2] Liang Jin-Jie, Gao Ning, Li Yu-Hong. Surface effect on \begin{document}${\langle 100 \rangle }$\end{document} interstitial dislocation loop in iron. Acta Physica Sinica, 2020, 69(3): 036101. doi: 10.7498/aps.69.20191379
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Publishing process
  • Received Date:  25 October 2010
  • Accepted Date:  28 February 2011
  • Published Online:  15 August 2011

Development of percentile estimation formula for skewed distribution

  • 1. College of Physics Science and Technology, Yangzhou University, Yangzhou 225009, China;
  • 2. National Climate Center, Beijing 100081, China

Abstract: Order statistics establishes a relation between the position of the ranked data and corresponding cumulative probability, so it can be used to estimate the cumulative probability. Owing to the fact that different climatological data have different skewness degrees, in this paper, according to the cumulative probability function under the skewed distribution conditions, we perform theoretical analysis and numerical simulation to establish the position parameters of the regression model which are related to skewness index, then give an amperic percentile formula under the skewed distribution. By using the data about the summer temperature in global from 1980 to 2009, we compare the positions of ranked data corresponding to the 90th percentile, which are obtained by this formula and Jenkinsons formula.

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